The solutions to 9, 10, 11 and 12 magic sums are
shown in the illustration.

The solution of magic sum 10 was sent to us
separately by Jocelyne Yataco, Peter Fenner and Stephen Merriman with
Michelle Curl as an improvement to our wrong previous condition to
this puzzle which stated that the magic sum of 10 was impossible to
reach for this triangle. We were wrong and now with the help from our
visitors we improve our mistake. Thanks!